Impact of Stellar Companions on Precise Radial Velocities⋆

A&A 550, A75 (2013) Astronomy DOI: 10.1051/0004-6361/201220083 & c ESO 2013 Astrophysics

Impact of stellar companions on precise radial velocities

D. Cunha1,2,P.Figueira1,N.C.Santos1,2,C.Lovis3, and G. Boué1,4

1 Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal e-mail: [email protected] 2 Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal 3 Observatoire Astronomique de l’Université de Genève, 51 Ch. des Maillettes, 1290 Sauverny, Versoix, Suisse 4 ASD, IMCCE-CNRS UMR 8028, Observatoire de Paris, UPMC, 77 avenue Denfert-Rochereau, 75014 Paris, France Received 23 July 2012 / Accepted 29 November 2012

ABSTRACT

Context. With the announced arrival of instruments such as ESPRESSO one can expect that several systematic noise sources on the measurement of precise radial velocity will become the limiting factor instead of photon noise. A stellar companion within the fiber is such a possible noise source. Aims. With this work we aim at characterizing the impact of a stellar companion within the fiber to radial velocity measurements made by fiber-fed spectrographs. We consider the contaminant star either to be part of a binary system whose primary star is the target star, or as a background/foreground star. Methods. To carry out our study, we used HARPS spectra, co-added the target with contaminant spectra, and then compared the resulting radial velocity with that obtained from the original target spectrum. We repeated this procedure and used different tunable knobs to reproduce the previously mentioned scenarios. Results. We find that the impact on the radial velocity calculation is a function of the difference between individual radial velocities, of the difference between target and contaminant magnitude, and also of their spectral types. For the worst-case scenario in which both target and contaminant star are well-centered on the fiber, the maximum contamination for a G or K star may be higher than 10 cm s−1, on average, if the difference between target and contaminant magnitude is Δm < 10, and higher than 1 m/sifΔm < 8. If the target star is of spectral type M, Δm < 8 produces the same contamination of 10 cm s−1, and a contamination may be higher than 1m/sifΔm < 6. Key words. techniques: radial velocities – planets and satellites: detection

1. Introduction Here we address a so far unexplored mechanism that is capable of distorting RV signals and creating false ones: the contam- The search for extrasolar planets is currently a very active field ination of the main spectrum by that of a (usually unresolved or of research in astronomy. Since the first discovery of Mayor otherwise undetectable) companion. We consider two different &Queloz(1995), more than 800 planets were discovered1,of cases: which 80% were detected with the radial velocity method (RV). Because it is the workhorse for planetary detections, this method 1. that of a faint gravitationally bounded companion; and received much attention from the community, which constantly 2. that of an unbound star that is aligned with the target at the increased its precision (for some of the latest results check moment of observation. Mayor et al. 2011) and tried to characterize its limitations. One of the fundamental drawbacks is that it is an indirect We assumed the target stars to be placed at the Galaxy disk edge method, and therefore one should be extremely careful with false to consider a representative case that encompasses several scenarios of contaminant stars. We used real high signal to noise ra- positives, i.e., signals created by other planetary RV signals. The / literature provides many examples and techniques used to pin- tio (S N) observations obtained with HARPS to create the com- point these signals (e.g. Queloz et al. 2001; Santos et al. 2002; posite spectra and process these with the RV calculation pipeline Melo et al. 2007; Huélamo et al. 2008; Figueira et al. 2010)or to evaluate the impact of the contamination in the most realistic way possible. While we aim at characterizing this effect down to to average them out (Dumusque et al. 2011b,a). With the ad- −1 vent of very high precision spectrographs, such as ESPRESSO the precision level of ESPRESSO, 10 cm s , it can be assessed or CODEX (Pepe et al. 2010), the RV precision enters a new at an even lower precision level. domain, that of cm s−1, which in turn will increase the quality Although this study is performed to characterize the impact on the RV when using the cross-correlation function (CCF), of our characterization of these unwanted yet ubiquitous signals ff (e.g. Cegla et al. 2012). point spread function (PSF) modeling will also be a ected by stellar companions, if in a different way. The results of this study are particularly interesting for deep surveys in crowded fields Appendices are available in electronic form at (Kepler). http://www.aanda.org If the contaminant RV remains constant, stellar blends will 1 http://exoplanet.eu/,asof27/09/2012 only cause a undetectable contamination in the RV calculation. Article published by EDP Sciences A75, page 1 of 14 A&A 550, A75 (2013)

However, if the contaminant RV is changing, if the seeing varies, Table 1. Probability of observing a binary with a mass ratio q = M2/M1 or if there are guiding problems during observations, the effect of among G-dwarf binaries for periods P < 104 days and P < 104. the contamination will no longer be constant and it might mimic the presence of a planet. As an example of a false positive caused qmax 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 by blended stars we refer to the work of Santos et al. (2002), in P < 104 days which RV measurements derived from CORALIE blended spec- P(q) [%] 12.0 16.3 13.1 12.7 12.3 12.9 6.5 1.9 2.6 3.4 6.2 tra of HD 41004 AB have unveiled a radial-velocity variation > 4 with a period of 1.3 days and a small amplitude of 50 m/s, com- P 10 days P(q) [%] 11.1 11.9 18.4 15.8 10.5 11.2 6.6 6.6 4.0 4.0 0 patible with the signal expected to be caused by a planetary companion to HD 41004 A. Another example is WASP-9b, which Total was discarded as a planet after it was discovered that the signal P(q) [%] 11.4 13.6 16.4 14.6 11.2 11.8 6.5 4.8 3.4 3.8 2.4 was due to a fortuitous alignment (Triaud, priv. comm.). Notes. From Duquennoy & Mayor (1991). In Sect. 2 we explain which stars we consider most likely to contribute to a shift in the RV calculation, if the star is either in a G-, K- or M-dwarf binary system, or is affected by a Table 2. Probability of observing a binary with an eccentricity e among G-dwarfs binaries for periods P < 103 days and P < 103. fortuitous alignment. Then, in Sect. 3 we describe the properties of the spectra used in our simulations. In Sect. 4 we describe the method used to scramble spectra from target star and stel- emax 0.15 0.3 0.45 0.6 0.75 0.9 1 lar companion. Results from our work, assuming the worst-case P < 103 days scenario in which both target and contaminant are well centered P(e) [%] 12.50 43.75 31.25 6.25 6.25 0.0 0.0 on the fiber, are shown in Sect. 5. The results are followed by a P > 103 days statistical analysis in Sect. 5.4, which is based on these results, P(e) [%] 5.88 11.76 23.53 14.71 20.59 23.53 0.0 but assumes a more realistic situation, in which the contaminant star may not be fiber centered. In Sect. 6 we discuss our work, Notes. From Duquennoy & Mayor (1991). and we present our conclusions in Sect. 7. Table 3. Probability of observing an M-dwarf binary with a mass ratio q = M2/M1. 2. Contaminant cases

qmax 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 When one observes a target star, a secondary star may be present, P(q) [%] 0.0 1.61 5.95 10.45 12.93 13.84 14.48 13.03 14.58 13.13 even without one’s knowledge. This secondary star may be a source of contamination for the calculation of the target star’s Notes. From Janson et al. (2012). RV. Secondary/contaminants stars may appear as two diﬀerent types: real binaries or fortuitous alignments. Table 4. Probability of observing an M-dwarf binary with a certain log a. 2.1. Real binaries log amax 0.25 0.5 0.75 1. 1.25 1.5 1.75 2. 2.25 2.5 In the case of a real binary system, the contaminant star will be P(log a) [%] 0.51 2.60 9.02 15.39 17.13 17.65 14.73 11.74 7.85 3.37 gravitationally bound. In this section we present the probability distributions of real binary properties that we used in our work. Notes. From Janson et al. (2012). Here, for G- and K primaries we based our study on the results of Duquennoy & Mayor (1991), who studied the For M-dwarfs we used the distributions of mass ratio, q, multiplicity among solar-type stars in the solar neighborhood. and semi-major axis, a, from the work of Janson et al. (2012) They considered a subsample of 164 primary stars with spec- on M-dwarf multiplicity. The authors suggest an M-dwarf to- tral types between F7 and G9. Using Table 7 of Duquennoy & tal multiplicity fraction of 34%. Table 3 shows the probability Mayor (1991) on the mass-ratio distribution among G-dwarfs of observing an M-dwarf binary with a mass ratio q.Jansonet binaries, we can calculate the probability of observing a binary al. found a uniform distribution to be more consistent with the with a mass-ratio q = M2/M1,whereM2 is the mass of the sec- mass ratio of their observed sample, than a rising distribution. ondary star and M1 the mass of the primary. These probabili- Accordingly, we assumed their uniform distribution in our work. ties are shown in Table 1, in which we can see that there is a For the semi-major axis distribution Janson et al. (2012)also maximum for the mass-ratio range ]0.2,0.3]. The distribution of compared the Sun-like and the narrow distribution, ﬁnding the orbital periods (P) of their study is approximated to a Gaussian latter to be more consistent with their sample. We therefore used with log P = 4.8andσlog P = 2.3. this distribution, which is shown in Table 4. As no information Duquennoy & Mayor also presented the eccentricity distri- was given on the eccentricity distribution for M-dwarf binaries, bution for P < 1000 and P > 1000 days, shown here in Table 2. we assumed the distribution from Duquennoy & Mayor (1991). We stress that there is a large uncertainty for VLMC (very These distributions were used in our statistical analysis low mass companion) binaries (with q < 0.1), and that this study (Sect. 5.4). does not include values of q below 0.01. We also emphasize that this mass ratio distribution is calculated for binary stars, but we 2.2. Fortuitous alignment recall that, also according to Duquennoy & Mayor (1991), there are 57% of binary systems with a mass ratio higher than 0.1, and Even if the target star is a single star, an alignment with a 43% of apparently single stars. Of these 43%, (8 ± 6)% most background/foreground object may occur. To study the prob- probably have a VLMC, which puts the percentage of single ability of such an event we used the Besançon model (Robin stars at ∼30%. et al. 2003). This allows one to compute the probable stellar

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Table 5. Most probable contaminants for the fortuitous alignments. 4. Method The goal of this work is to study possible stellar contamination Spectral type mV P [%] [F0, F5[ [13, 16] ∧ [20, 23] 0.08 of a target star. To do so, we co-added target and contaminant [F5, G0[ [13, 24] 1.25 spectra. We not only considered contaminant stars of spectral [G0, G5[ [13, 25] 1.74 types F2, F5, G2, G8, K0/K1, K5, M1, and M3, but also differ- [G5, K0[ [13, 25] 1.32 ent ratios of magnitude between target star and contaminant as [K0, K5[ [12, 26] 2.5 well as differences in RV. To sum two spectra with these partic- [K5, M0[ [16, 30] 4.48 ular conditions is not trivial. We need to control the magnitudes [M0, M5[ [17, 30] 16.99 and RVs. [M5, M8[ [20, 30] 12.12 , , We set the magnitude V of the target (mt) star according to [M8 M9] [21 30] 13.17 the data available in Simbad2 and then calculated the magnitude of the contaminant (mc) with respect to the target star using the Table 6. Stars used in our simulations, their spectral type, visual mag- apparent magnitude – flux relation. We also considered the rel- nitude (mv)andS/N at the center of the spectral order 50 (SN50). ative RV between the two spectra as a tunable knob. However, when processing our spectra using the HARPS pipeline the re- 1 duction takes into account the header (and properties) of the par- Object Spec.Type mv SN50 HD 20852 F2 6.92 225; 98 ent spectra. To overcome this situation we calculated the contam- HD 103774 F5 7.12 102; 146 inant RV in the target reference frame and shifted it afterwards. Sun G2 3.652 225; 260 We then co-added the target spectrum with the modified Tau Ceti G8 3.50 300; 450 contaminant spectra and processed the result with the HARPS HD 69830 K0 5.95 253; 380 RV pipeline. Alpha Cen B K1 1.33 385; 399; 302 More details of the method are presented in Appendix B. HD 85512 K5 7.65 156; 86 Gl436 M1 10.68 15; 31; 46 Gl581 M3 10.57 37; 22 4.1. The “real binaries” star strategy

(1) Notes. from Simbad (http:simbad.u-strasbg.fr/simbad/ To study the impact of a companion on the RV calculation of sim-fid). (2) m of the moon within the HARPS 0.5 radius fiber. v a binary primary star, we reproduced the cases discussed in the work of Duquennoy & Mayor (1991). We considered a primary G2 star with six different secondary/contaminant stars: G2, G8, content on a given direction of the Galaxy, permitting one to K1,K5,M1,andM3. infer the most probable contaminants. To do so, we simulated The first case had a G2 as contaminant with positive and neg- an observation in the direction of the HD 85512 coordinates, Δ = − ative values of RV RVCc RVCt,whereRVCt is the target (l, b) = (271.6759, 8.1599), which is positioned at the border barycentric radial velocity (drift corrected) without contamina- of the Galactic disk. We also considered a distance interval of tion, and RVCc is the contaminant barycentric radial velocity 50 kpc (approximately the diameter of the Milky Way), mag- (drift corrected) in the target reference frame. In Fig. 2 we show nitudes between 0 and 30, and a solid angle for a radius of 3◦. − the impact, RVCt RVCt , of the stellar companion on the target The objective was to have a large number of stars for each bin of RV, where RVCt is the target barycentric radial velocity (drift magnitude and spectral type and then to divide it by the ratio be- corrected) with contamination. tween the area considered and that for the HARPS fiber (radius For each target-contaminant pair we considered a range of of 0.5 arcsec), thus obtaining the density of stars or the prob- |ΔRV| between 0 and 30 [km s−1](instepsof1[kms−1]), except ability to have a fortuitous alignment within the HARPS fiber. for a secondary star of spectral type K5 in which the maximum In Fig. 1 we present a contour plot of the total number of stars |ΔRV| was of 24 [km s−1] (see Appendix B for details). obtained in the simulation for each bin of magnitude and spectral type. For more details on these values and the values for the star density when normalized for a HARPS size fiber, see 4.2. Fortuitous alignment strategy Appendix A. The most probable contaminants for the accidental alignments are shown in Table 5. The fortuitous alignment case is more generic. Here we considered six spectral types of primary stars (G2, G8, K0, K5, M1, and M3) in combination with the eight spectral types as contam- 3. Data inants – the same six used as target stars plus an F2 (HD 20852) and an F5 (HD 103774) star. For each spectral type of primary We contemplated target stars from spectral type G to late M, stars we considered contaminants with magnitudes mv between 5 with visual magnitudes, mv, between 5 and 15. As described in and 15 (in steps of one). The contaminants considered were the previous section (Sect. 2.2), the most probable contaminant those described in Table 5. stars are of spectral types FGKM. To represent both target and Although the Besançon model includes oxygen and carbon contaminant spectral types, we chose spectra from nine stars, AGB (asymptotic giant branch) stars and white dwarfs in the whichareshowninTable6. search, we only considered main-sequence (MS) stars. Very We used spectra with an S/N at the center of the spec- metal-poor stars were also excluded from our study. For an M1 tral order number 50 (which corresponds to a wavelength of target star a K0 star (HD 69680) was used instead of the K1 437.28 nm), varying between 15 for an M star, and 450 for a mentioned above. This was because the barycentric Earth radial Gstar.TheS/N values of these spectra can be found in Table 6. velocity (BERV) value form the K1 star did not allow the desired The stars were chosen because they had the highest S/Nintheir spectral type range, as observed with HARPS. 2 http://simbad.u-strasbg.fr/simbad/sim-fid

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Fig. 1. Number of stars in each bin of spectral type and magnitude (radius of 3◦).

5. Results 5.1. Real binaries The results for the contamination by the secondary star of a binary with a primary star of spectral type G2 as a function of ΔRV can be found in Fig. 3. Obviously, the impact on the RV calculation is a function of the difference between target and contaminant RV (ΔRV). One can interpret a CCF as an “average” line of a spectrum, that is fittedbyaGaussiancurveto measure the center of the CCF. In the presence of a second star, the CCF is composed of two curves. For ΔRV = 0thetwo curves fully overlap, and so the impact on the Gaussian fit and on the RV calculation is minimum. As ΔRV increases, the impact on the Gaussian fit increases until the point when the two | | CCF curves overlap, with the contaminant RV, RVCc , close to 0.6 times the FWHM of the target CCF. When the CCF curves become distinct, the impact on the measured RV of the primary decreases. For |ΔRV| > 20 km s−1 the peak of the contaminant CCF curve exits the CCF window that is usually computed with Fig. 2. Shift of a G2 target RV caused by a contaminant of the same a value of 20 km s−1, and for values |ΔRV|≥25 km s−1 the con- ff spectral type and magnitude, mv, in function of the di erence between taminant CCF curve completely exits the target CCF window. individual radial velocities. Nevertheless, the contamination is not null. There are bumps in the wings that slightly contaminate the target spectra. Figure 4 shows the maximum contamination for each type of contaminant. As we can see, as the secondary stars become fainter and of later spectral type, the maximum contamination decreases. shift in RV. For each target-contaminant pair we considered the differences between its RV, |ΔRV|, under 20 km s−1, which is half the width of the CCF window. Although giant stars will often be 5.2. Contamination by the sky contaminant stars, we assumed that spectra from MS stars are similar to those of giants and used only spectra of MS stars in The sky brightness is not zero and its light results from the re- our simulations. flection and scattering of Sun spectra. The sky brightness has a

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Fig. 3. Impact on the RV of a G2 target star caused by a companion of spectral type G2, G8, K1, K5, M1, and M3 (left to right, top to bottom). For each case a close-up with a bump for the impact for 10 < ΔRV < 24 km s−1 is shown.

2 magnitude per arcsec in V band of 21.8 on a new-moon night, them (Δm = mc − mt), as we can see in Fig. 6. This way, we only and of 20.0 on a full-moon night. To study the impact of this con- carried out our study on the impact for a target star in which mv tamination we assumed that sky spectrum is the solar one. This differs |Δm| from the contaminant star. The result of our study for is equivalent to say that for a fiber of 0.5 radius, we have a sys- contamination as a function of spectral type is shown in Fig. 7. tematic contamination of a G2 star with mV ∼ 20 on a full-moon We first note that there is a clearly defined relation between night to a limit of a G2 star with mV ∼ 22 (new moon). Δm and the maximum of the contamination, except for some ff The results of the maximum contamination by the sky bright- cases where the di erence in magnitude between target and con- ness study are shown in Fig. 5. We can see that when observing taminant is null. A misidentification of the companion correlation peak with that of the primary may happen due to a (slightly) a G2, G8, K0, or a K5 target star fainter that mV = 11, or M1, larger contrast. If we take only Δm > 1, we can describe the M3 fainter that mV = 14, the errors induced on the observed RV − Δ can be larger than 10 cm s 1, which can be a problem for future relation between m and the maximum of the contamination as instruments such as ESPRESSO. For a night of observation with − | − | = a·Δm+b, a full moon, induced errors become larger than 10 cm s 1 for G- Max RVCt RVCt 10 (1) and K target stars fainter that m = 9 and for an M star fainter V ffi than mV = 12. where a and b are the coe cients presented in Table 7.Inthis table we also present the value for the root mean square (rms) for each fit. By comparing the panels of Fig. 7 we can also 5.3. Fortuitous alignment see that the contamination depends not only on Δm,butalso on the target-contaminant spectral type combination. This be- In this section we present a more exhaustive study of all pos- comes more evident in Fig. 8. This figure shows the maximum sible sources of stellar contamination. Beyond the moon as a contamination as a function of the contaminant spectral type for contaminator, there is a vast range of possible contaminators, as a G2 and M3 target star with Δm = 10. We find two reasons was discussed in Sect. 2.2. Our study is simplified because our for this behavior. First, less contamination occurs with increas- analysis holds for similar spectra with different magnitude for ingly different spectra. Also, the contamination will depend on target and contaminant star, but with same difference between the depth of spectral line. Thus, for similar spectra, cooler stars

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5.4.1. Statistical analysis of binaries For our statistical analysis of contamination in binary systems, we considered the mass ratio distributions, q, mentioned in Sect. 2.1.WeusedTable1 based on the study of Duquennoy & Mayor (1991) for target stars of spectral types G and K, and Table 3 based on the study of Janson et al. (2012)fortarget stars of spectral type M. Because we had M1 and M3 spectra for M stars, we used the M1 spectra for [M0, M4[ stars, and for the later types we used the M3 spectrum. From the work of Duquennoy & Mayor (1991)andJanson et al. (2012) we also used the probability density function for the orbital period and for the eccentricities (see Table 2) for G dwarfs, and the probability density function for the semi-major axis for M-dwarfs (see Table 4). The projected distance R and the ΔRV were drawn performing a Monte Carlo simulation of Kepler’s laws and its projection, considering a uniformly random mean anomaly (M ∈ [0, 2π]), inclination (cos i ∈ [−1, 1]), longi- tude of the node (Ω ∈ [0, 2π]), and argument of the periapsis (ω ∈ [0, 2π]). To compute the luminosity of the stellar companion given Fig. 4. Maximum contamination of a G2 target star caused by each com- the mass of the star, we used relation 2 from Duric (2003): panion spectral type in m/s. ⎧ . ⎪ L M 4 0 ⎨⎪ ∝ if M > 0.43 M ; L M ⎪ . (2) ⎪ L M 2 3 ⎩ ∝ . , M < . M . L 0 23 M if 0 43 will cause a higher contamination, because their spectral lines depth is higher. 5.4.2. Statistical analysis of fortuitous alignments For the fortuitous alignment we are only interested in contaminant stars whose flux can enter the fiber. With a seeing of 0.93, 5.4. Statistical analysis of the contamination which is the mean value for the La Silla observatory, we measured that the fraction of flux that enters the fiber of a star at After calculating the impact caused by a contaminant star in the 2.6 arcsec from the fiber center is 2 × 10−8. If target and contam- RV calculation, it is important to known how often this occurs. inant star have the same magnitude, this corresponds to an effec- Therefore we calculated the probability of measuring the target tive Δm of 19 within the fiber, and so its impact on the target RV RV with a given contamination. can be considered null for our purpose. We then created a prob- In the previous two subsections (Sects. 5.1 and 5.3)wepre- ability density function to have a contaminant star of a certain sented a study for the impact to have a contaminant star within spectral type and magnitude within a radius of up to 2.6 arcsec the fiber on the RV calculations, assuming that the fiber was around the target star, using the density tables from Appendix A. well centered on target and contaminant. Although this is a rel- For background/foreground stars within the 2.6 arcsec ra- evant study, the most probable scenario for real observations is dius we assumed a uniform distribution, and if a contaminant that of a contaminant star that not centered in the fiber. In this is present, the probability that the star is standing at a distance r case, we cannot consider that both target and contaminant fluxes from the target is proportional to r2, and the probability to have will completely enter the fiber, and therefore we calculated how the fortuitous contaminant star between r and r + dr is given by much of each flux enters the fiber. The fraction of binary and for- Eq. (3): tuitous alignments and their properties also follows established probability laws. To take these parameters into account in a real- P(r, r + dr) = π 2rdr + dr2 , (3) istic way, we ran Monte Carlo simulations with 10 000 trials, to calculate the distribution function of the impact of the presence in which the members are self-explanatory. of a contaminant star on the RV calculation. Once again, we had To calculate ΔRV we used the probability density function to consider both cases of contamination: binaries and fortuitous for the systemic RV, which was computed by fitting a Gaussian alignment. If in our simulations one star was in a binary sys- to the systemic velocity of stars from HARPS. This yielded an tem and had a background/foreground at the same time, we only average and a dispersion of (μ, σ) = (7.87, 29.87). considered the stronger RV effect. In these simulations we did not take into account the contamination by the sky brightness ei- 5.4.3. Statistical analysis results Δ ≤ −1 ther, and also just considered that only RV 20 km s will The probability to have a given impact on the RV calculation for produce a significant impact. We ran the simulations for each each case is presented in Fig. 9. We can see that the most prob- case of spectral type target considered in previous sections, at a able scenario is to have a contamination of less than 10 cm s−1. = , , , , distance d 1 5 10 50 and 100 [pc] from Earth. But contamination may happen and is more probable for far- Before presenting our results of the statistical analysis we away target stars, either because they become fainter, or be- describe in more detail the considerations to statistically an- cause, in the case of a binary star, it is more probable that the alyze the real binaries (Sect. 5.4.1) and fortuitous alignments companion star flux enters the fiber. We can examine the target (Sect. 5.4.2). star G8, for instance. In this case, if the target star is 100 pc

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(a) (b)

(e) (f)

Fig. 5. Maximum contamination of the sky brightness on a a) G2, b) G8, c) K0, d) K5, e) M1, and f) M3 target star spectra. The blue triangles show the impact on the RV caused by the sky brightness on a full-moon night, while black diamonds show the impact on a new-moon night. away, there is only a probability of 67% for a contamination 6. Discussion below 10 cm s−1, and 14% probability for a contamination between 10 and 100 m/s. There is a peak around a contamina- We showed that we should not neglect the possibility that a stel- − tion of 103 cm s 1, which is, very probably, caused by physical lar companion contaminates the RV calculations. This is spe- binary contamination. This level of contamination needs to be cially true for far-away stars, which have a higher probability taken into account when choosing targets for planet searches. to have two stars within the ﬁber. Nevertheless, we stress some This becomes even more important when choosing target stars assumptions we made that may have some impact on our work. to be observed with ESPRESSO. Because spectra with high SN are scarce for late-M stars, in our

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never cause an impact higher than 100 m/s, and an impact of tens m/s is only possible if target and contaminant have almost the same magnitude (Δm 1.5). On the other hand, even for actual precisions, we may reach a potentially detectable contamination due to a Δm = 9. In many cases the induced effect is not detectable because it is a constant effect. Nevertheless, there are conditions (variable seeing, centering and/or pointing problems, etc.) in which the induced effect will not be constant. Even so, a very particular configuration is necessary (and is highly un- likely) for the effect to create a periodic signal. A contamination stronger than 1 m/s on the RV calculation of a K0 target star is possible if Δm < 9. If the K0 star is at 10 pc, it will have a mv ∼ 6, which means that contaminant stars with 6 ≤ v ≤ 15 can cause such a contamination. The probability to have one contaminant star with 6 ≤ mv ≤ 15 within the 0.5 radius fiber is 0.02% only. These tabled effects correspond to the maximum case, i.e., to the difference between contamination and no contamination. Fig. 6. Contour plot of the maximum induced RV shift in the target Discussed cases are extreme in the sense that they are contam- |RVC -RVC| depending on the target (m ) and contaminant (m )mag- t t t c ination and no contamination. Nevertheless, to extensively ana- nitudes. lyze a variable contamination impact we would need to perform many hypotheses with uncertain parameters, such as seeing or flux counts. statistical analysis we used the M1 spectra to represent the [M0, M5[ bin and the M3 spectra for the [M5, M9]. We also assumed that the star will have at most one stellar companion, because 6.1.1. Sky brightness we found that the probability to have two contaminant stars is too low. We also did not take into account the effect of the sky In our analysis of the sky brightness impact we assumed that sky brightness if there was no stellar companion. brightness is mainly caused by the moon, and so its spectra will We also stress that the Besançon model is a probabilistic be that of a star with spectral type G2. The new-moon sky bright- model, and thus is not free of errors. We consider it reasonable ness should then be considered as a lower limit for the contami- that the distribution of fortuitous alignments is a Poisson√ distri- nation from the sky brightness with a G2 spectrum. However, we bution of stars. Thus, the associated error is equal to N,where should not forget that sky brightness has other sources and may N is the number of stars per area element. depend on the sky zone. Sky spectra from the Galactic disk are surely different from the Galactic halo. Moreover, there is also The results presented in Fig. 7 may lead one to think that the possibility to have a galaxy as contaminant, which was not contamination may be stronger than it actually is, but we should considered. Nevertheless, we consider it a good approximation, not forget that this figure only shows the maximum impact or at least a good starting point, to treat the sky brightness as a of contamination as a function of Δm, which occurs when G2 star. |RV(contaminant)|∼0.6 × FWHM(target). We also considered that both stars are well-centered in the fiber and that all flux en- If observations are carried out on a night with moon, and ters the fiber. This justifies our statistical analysis for the im- if cirrus are present, the contamination by the moon will be pact of the stellar companion within the fiber. With our statisti- enhanced. cal analysis we are able to conclude that it is important to take Tripathi et al. (2010), reported two outlier RV data points into account the possibility of contamination by a stellar com- caused by cirrus during their observations of WASP-3, an F7 star of mv = 10.7, on a full-moon night. Their RV measurements panion within the fiber, especially when the RV precision enters / / the domain of the cm s−1. Although the probability to have a con- present a redshift of 140 m s and of 49 m s with respect to their tamination lower than 10 cm s−1 is above 50% for every target best-fitting models. If we assume that cirrus will reflect some of the moonlight, we have a G2 contaminant. The maximum value star considered, we should pay special attention to far-away tar- ff get stars, for which the impact of contamination can be higher considered for all practical e ects for the visual magnitude of than 10 cm s−1 for 30−40% of the cases. this contaminant will be that of the target star (if it were higher than the target magnitude, the target star would be no longer visible). Thus, for a G2 target star with mv = 10.7 and a contam- 6.1. Impact on typical cases inant with the same spectral type and magnitude, the maximum contamination will be 2.7 km s−1. This corresponds to 0.15% As a consequence of the results presented in Fig. 7,wepresent of the moonlight flux, considering that 100% of the moonlight in Table 8 a study on the limit Δm for which the maximum im- flux corresponds to a star of magnitude 3.65. If 0.01% of the pact on the RV calculation is higher than 10 cm s−1, 1, 10, and moonlight reaches the fiber, corresponding to a contaminant of 100 m/s. From this table we can see that for a G star with a spectral type G2 with mv = 13.7, the contamination would be contaminant M star, an impact higher than 100 m/s only occurs 140 m/s. For a contamination of 49 m/s, 0.003% of the moon- if Δm < 2. However, in Table 5 from Sect. 2.2 we have seen light flux would be enough, corresponding to a G2 contaminant = . that the probability to have a contaminant M star of mv < 17 is with mv 14 8. Because the Tripathi et al. (2010) data were very low. Thus, if we are only interested in target stars brighter taken with the High Resolution Échelle Spectrometer (HIRES) than mv = 15, an impact higher than 100 m/sisveryunlikely. on the Keck I telescope, and we used HARPS spectra in our We can also see that when observing an M star, an F star can simulation, and also because we did not calculate the impact for

A75, page 8 of 14 D. Cunha et al.: Impact of stellar companions on precise radial velocities

(a) (b)

(e) (f)

Fig. 7. Maximum impact of |Δm| on the |RVCt| for a target star of spectral type a) G2, b) G8, c) K0, d) K5, e) M1, and f) M3, and contaminants of spectral types F2 (star), F5 (hexagon), G2 (squares), G8 (diamonds), K1 (circles), K5 (triangles), M1 (× crosses), and M3 (+ crosses). a target of spectral type F, these contamination values are pre- The sky brightness contamination is not easily removed. sented here just as a reference, since we cannot directly compare Although its signal may be strong enough to contaminate the them. Nevertheless, we consider that their hypothesis of cirrus RV calculations, it will be too weak to be adequately character- contamination is valid. ized, ﬁtted, and removed, even for a long-slit spectrograph.

A75, page 9 of 14 A&A 550, A75 (2013)

Table 7. Coeﬃcients a an b for each ﬁtting of the relation between Δm Table 8. Limit Δm for which the maximum impact (Imax)onthetarget | − | = / and the maximum impact on the RV calculations: Max RVCt RVCt RV is higher than 0.1, 1, 10, and 100 m s, for each combination of target 10a·Δm+b, and rms resulting from each combination of target spctral type spctral type (TST) and contaminant spectral type (CST). (TST) and contaminant spectral type (CST). CST / TST CST ab rms TST Imax[m s] F2 F5 G2 G8 K0 K5 M1 M3 [cm s−1] G20.11010111111109.59.5 G2 F2 −0.4008 5.0733 815.0813 1 88999877 F5 −0.4019 5.1601 1644.9045 10 5.5 5.5 6 6 6 5.5 4.5 4.5 G2 −0.4022 5.4288 4491.1375 10033444322 G8 −0.4023 5.4829 4956.4768 G8 0.1 10 10 11 11 11 10.5 9.5 9.5 K1 −0.4026 5.4556 5136.0605 1 7.5 7.5 8.5 8.5 8.5 8 7 7 K5 −0.4009 5.1859 1500.0546 105566 65.54.54.5 M1 −0.4001 4.8096 23.3793 100 2.5 2.5 3.5 3.5 3.5 3 2 2 M3 −0.3996 4.7301 197.1604 K0 0.1 9.5 9.5 11 11 11 10.5 9.5 9.5 G8 F2 −0.4008 4.9379 681.0614 1 7.5 7.5 8.5 8.5 8.5 8 7.5 7.5 F5 −0.4019 5.0222 1075.0923 10 4.5 5 6 6 6 5.5 4.5 4.5 G2 −0.4027 5.3440 3968.9098 100 2.5 2 3.5 3.5 3.5 3 2 2 G8 −0.4021 5.3154 2697.4956 K5 0.1 10 10.5 11 11.5 11.5 11 10 10 K1 −0.4027 5.3641 4215.8544 1 7.5 8 8.5 9 9 8.5 7.5 7.5 K5 −0.4007 5.11 1139.4446 1055.566.56.56 5 5 M1 −0.3995 4.7357 3.0972 100 2.5 2.5 3.5 4 4 3.5 2.5 2.5 M3 −0.3984 4.651 51.5545 M1 0.1 6.5 6.5 7.5 8 8 8.5 10.5 10.5 K0 F2 −0.3812 4.7320 1566.6309 1 4 4 5.5 6 5.5 6.5 8 8 F5 −0.4008 4.9521 871.3506 10 1.5 1.5 3 3 3 4 5.5 5.5 G2 −0.3933 5.2712 5307.563 100 – – 0.5 0.5 0.5 1.5 2.5 2.5 G8 −0.3929 5.2613 4246.1257 M3 0.1 6.5 6.5 7.5 8 8 9 10.5 10.5 K1 −0.3954 5.3704 7390.8788 1 3.5 3.5 5 5.5 5.5 6.5 7.5 7.5 K5 −0.3914 5.1827 3347.1766 10 1 1 2.5 3 3 3.5 5 5 M1 −0.3799 4.7540 566.5518 100 – – 0 0.5 0.5 1.5 2.5 2.5 M3 −0.3777 4.6783 532.1239 K5 F2 −0.3988 4.9559 200.036 F5 −0.3999 5.0865 724.4446 G2 −0.4035 5.4592 7366.4185 G8 −0.4032 5.5354 8587.4134 K1 −0.4053 5.5580 14 146.5377 K5 −0.4030 5.3793 4935.42 M1 −0.4011 4.9458 71.0313 M3 −0.4009 4.9257 98.6394 M1 F2 −0.4056 3.5177 18.1497 F5 −0.3932 3.4673 24.6295 G2 −0.4018 4.1212 10.1997 G8 −0.4011 4.2786 13.0058 K1 −0.3990 4.1604 24.4166 K5 −0.4014 4.5525 19.9346 M1 −0.3985 5.0993 33.3093 M3 −0.3994 5.1581 56.2493 M3 F2 −0.4052 3.4770 14.7829 F5 −0.3924 3.4421 25.7393 G2 −0.4035 4.0854 30.8372 G8 −0.4019 4.2469 23.5459 K1 −0.4024 4.2649 35.7392 − K5 0.4021 4.5317 32.2298 Fig. 8. Maximum contamination |RVC − RVC| as a function of the M1 −0.3991 5.0440 13.2551 t t − contaminant spectral type for a G2 (blue dots) and M3 (green diamonds) M3 0.3999 5.1436 63.9946 target star with Δm = 10.

6.1.2. Kepler stars to detect a second peak on the CCF and concluded that the Our work can also be a valuable asset for the follow-up of pro- two stars probably have nearly the same RV. They computed / grams such as Kepler. Kepler stars have 11 mv 18 (see an impact of 280 m s on the RV caused by the companion star. Batalha et al. 2012), and consequently, measuring the RV be- A direct comparison with their work is not possible, because comes challenging. Beyond the problem of these being faint their observations were carried out with the Fiber-fed Échelle stars, there is also the problem of the false-positive planet transit. Spectrograph (FIES) at the 2.5 m NOT at La Palma, and with As an example, we consider the case of Kepler-14b (Buchhave the HIRES mounted on the Keck I on Mauna Kea, Hawaii. et al. 2011), a planet orbiting an F star with a companion star of Moreover, our simulation only contemplates target stars of spec- nearly the same magnitude and only 0.3 arcesec of sky-projected tral GKM, and this is an F star. Still, performing a rough compar- angular separation. Buchhave and collaborators were not able ison, we see that our simulations indicate an impact of ∼276 m/s

A75, page 10 of 14 D. Cunha et al.: Impact of stellar companions on precise radial velocities

(a) (b)

(e) (f)

| − | | | Fig. 9. Close-up of the distribution of the expected contamination, RVCt RVCt , on the radial velocity, RVCt , of a target star of spectral type a) G2, b) G8, c) K0, d) K5, e) M1, and f) M3, and at distance d, caused by a background or a companion star. The green thick solid line shows the distribution if the target star stands at a distance of d = 1 pc, the blue dotted line for d = 5 pc, black dashed line for d = 10 pc, magenta dash-dotted line for d = 50 pc, and red solid line for 100 pc. Numbers in each bin correspond to the impact probability for each target distance: the number in the top corresponds to 1 pc and the number in the bottom to 100 pc.

A75, page 11 of 14 A&A 550, A75 (2013) for a G2 target star with a contaminant of the same spectral type, Acknowledgements. This research has made use of the SIMBAD database, op- Δm = 1, and ΔRV = 1. erated at CDS, Strasbourg, France. D.C., P.F., N.C.S., and G.B. acknowledge the support from the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953, as well as from Fundação para a Ciência e a Tecnologia (FCT), Portugal, in the form of grant reference 7. Conclusions PTDC/CTE-AST/098528/2008. We also thank J.S. Amaral for a critical reading of the manuscipt. This study on the impact of stellar companions within the fiber of RV calculations allows us to conclude that we should not neglect References the possibility of contaminant flux from stellar companions stars, specially if we are observing far-away stars. On average, if we Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2012, ApJS, submitted [arXiv:1202.5852] are observing a G or a K star, the contamination may be higher Buchhave, L. A., Latham, D. W., Carter, J. A., et al. 2011, ApJS, 197, 3 −1 than 10 cm s if the difference between target and contaminant Cegla, H. M., Watson, C. A., Marsh, T. R., et al. 2012, MNRAS, 421, L54 magnitude is Δm < 10, and higher than 1 m/sifΔm < 8. If Dumusque, X., Santos, N. C., Udry, S., Lovis, C., & Bonfils, X. 2011a, A&A, the target star is a star of spectral type M, a Δm < 8 is enough 527, A82 −1 Dumusque,X.,Udry,S.,Lovis,C.,Santos,N.C.,&Monteiro,M.J.P.F.G. to obtain the same contamination of 10 cm s , and a contam- 2011b, A&A, 525, A140 ination may be higher than 1 m/sifΔm < 6. We also showed Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485 that sky brightness should not be discarded, particularly on full- Duric, N. 2003, Advanced Astrophysics (UK: Cambridge University Press) moon nights, if one observes faint target stars (mv > 10). Figueira, P., Marmier, M., Bonfils, X., et al. 2010, A&A, 513, L8 These results will allow us to more wisely choose tar- Huélamo, N., Figueira, P., Bonfils, X., et al. 2008, A&A, 489, L9 Janson, M., Hormuth, F., Bergfors, C., et al. 2012, ApJ, 754, 44 get stars to be observed with instruments such as ESPRESSO Mayor, M., & Queloz, D. 1995, Nature, 378, 355 and CODEX, and they provide reference values for the differ- Mayor, M., Marmier, M., Lovis, C., et al. 2011, A&A, submitted ent cases of contamination possible in fiber-fed high-resolution [arXiv:1109.2497] spectrographs. We also stress that there are diagnosis methods Melo, C., Santos, N. C., Gieren, W., et al. 2007, A&A, 467, 721 Pepe, F. A., Cristiani, S., Rebolo Lopez, R., et al. 2010, in SPIE Conf. Ser., 7735 that should be capable of detecting most of the blends that mim- Queloz, D., Henry, G. W., Sivan, J. P., et al. 2001, A&A, 379, 279 ick planets. We can detect a blend through bisector analysis of Robin, A. C., Reylé, C., Derrière, S., & Picaud, S. 2003, A&A, 409, 523 the CCF or from correlations using different templates (Santos Santos, N. C., Mayor, M., Naef, D., et al. 2002, A&A, 392, 215 et al. 2002). Tripathi, A., Winn, J. N., Johnson, J. A., et al. 2010, ApJ, 715, 421

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A75, page 12 of 14 D. Cunha et al.: Impact of stellar companions on precise radial velocities Appendix A: Density of stars

Fig. A.1. Number of stars in each bin of spectral type and magnitude for an area of the sky with a radius of 3◦.

Fig. A.2. Density of stars in each bin of spectral type and magnitude for an area of the sky with a radius of 0.5 arcsec.

A75, page 13 of 14 A&A 550, A75 (2013)

Appendix B: Method details assess by how much the contaminant spectra had to be shifted, we used Eq. (B.3) To control the magnitude of the contaminant star we first used the relation (B.1) to calculate mv in the target reference frame, RVC − RVC − ΔRV λ = λ × 1 + c t , (B.3) c t c mt − mc = −2.5 × log(Ft/Fc), (B.1) where λc are the new wavelengths to derive the desired ΔRV (difference between the RV of the target and the contaminant), λt are where Ft and Fc are the fluxes of the target and of the contaminant. The magnitudes are now calibrated and can be changed by the wavelengths from the wave file corresponding to the target, multiplying the flux by a factor of and c is the light speed in vacuum. These new wavelengths were used to calculate, by linear interpolation, the number of pixels by which the contaminant needed to be shifted. This gives a new f = 10−x/2.5, (B.2) xx axis that it was used, recurring to another linear interpolation, to shift the contaminant spectra. With the target RV for the con- where x is the difference between the new chosen magnitude and taminant, the next step is the sum of the target with the modified the true magnitude of the star in the target-star system. contaminant spectra, which is the sum of their fluxes. The shift of To change the RV of the contaminant spectra we also had to the contaminant spectra should not be larger that the maximum modify them. The first challenge when processing our co-added barycentric Earth radial velocity (BERVMX) of the star, other- spectra with the HARPS RV pipeline is that it will take into ac- wise there is the risk that the spectral lines enter and leave the count the header (and proprieties) of the parent spectra. To com- orders when performing the CCF calculation. BERVMX defines pensate for this we first need to replace the header of the con- the excluded spectral lines from the correlation due to the orbital taminant spectrum file with that from the target, and then run the movement of the Earth toward the star. Our goal is to introduce cross correlation function (CCF) recipe of the RV pipeline. The a shift equivalent to a BERV value lower than the |BERVMX|, next step in this process was to shift the contaminant spectra. To so that we do not need to exclude new lines.

A75, page 14 of 14